Unfortunately, it's unlikely you can get them back. Browser saves are really volatile. It'll be more reliable if you download the game to play it instead.
Alas, as I mentioned, that didn't work. If there's any chance that they might be findable, do you have any idea where I should look? I have the version of Windows that generally puts everything into AppData under your username, but I didn't see any file names in there that suggested LD or Newgrounds or anything.
Some more information that might be useful to you...since I can't get Newgrounds to load at all on Firefox most days (likely due to issues with the adblock that's built into that browser and possibly broken from the update), I tried using other browsers. On Chrome it works adequately well, but Edge slows to a crawl while attempting to play the game, probably because of a certain animated ad that Newgrounds plays on the page below the game window. And all three browsers appear to have separate save slots, which were blank before I started playing them...I still wonder if my old Firefox saves are just hidden somewhere, or if they've actually been deleted/overwritten.